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y(x)=x⁴+3x²-6
The derivative of the function/ y(x)=x⁴+3x²-6

Derivative of y(x)=x⁴+3x²-6

Function f() - derivative -N order at the point
v

The graph:

from to

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The solution

You have entered [src] 
 4      2    
x  + 3*x  - 6
$$x^{4} + 3 x^{2} - 6$$ 
d / 4      2    \
--\x  + 3*x  - 6/
dx
$$\frac{d}{d x} \left(x^{4} + 3 x^{2} - 6\right)$$
Transform
Detail solution

  1. Differentiate term by term:

    1. Apply the power rule: goes to

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    3. The derivative of the constant is zero.

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   3      
4*x  + 6*x
$$4 x^{3} + 6 x$$
Simplify
The second derivative [src] 
  /       2\
6*\1 + 2*x /
$$6 \cdot \left(2 x^{2} + 1\right)$$
Simplify
The third derivative [src] 
24*x
$$24 x$$
Simplify
The graph
Derivative of y(x)=x⁴+3x²-6
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